Parametric amplification of electromagnetic signals with superconducting transmission lines

Abstract

Amplification is required to detect small microwave signals. One new promising technology to achieve large amplification with quantum-limited noise is the kinetic inductance traveling-wave parametric amplifier (KI-TWPA). Through this superconductor device, amplification is obtained from a non-linear current wave equation undergoing a wave-mixing process where a pump and a target signals are injected. However, the amplitude equations used to design them are not complete. Indeed, they do not fully consider the complex nature of the propagation constant and characteristic impedance, relevant in periodic TLs. These two problems are tackled in this thesis with the goal of unveiling the optimal design process for KI-TWPAs. Firstly, the multiple-scales-method is explained and applied to the non-linear wave equation in four-wave-mixing. As a result, different models of amplitude equations are derived, together with the emergence of the idler and third pump s harmonic signals. It is demonstrated that the former is required in order to obtain amplification, while the latter is undesired. Furthermore, the total phase mismatch between the target, idler, and pump signals is identified as the main factor for achieving amplification. Thereafter, simulations results with each of the models are shown for different designs, from which a guide for optimal design is presented.